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CHAPTER (III) KINEMATICS OF FLUID FLOW

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CHAPTER (III) KINEMATICS OF FLUID FLOW 3.1: Types of Fluid Flow. 3.1.1: Real - or - Ideal fluid. 3.1.2: Laminar - or - Turbulent Flows. 3.1.3: Steady - or - Unsteady ... – PowerPoint PPT presentation

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Title: CHAPTER (III) KINEMATICS OF FLUID FLOW


1
CHAPTER (III) KINEMATICS OF FLUID FLOW
  • 3.1 Types of Fluid Flow.
  • 3.1.1 Real - or - Ideal fluid.
  • 3.1.2 Laminar - or - Turbulent Flows.
  • 3.1.3 Steady - or - Unsteady flows.
  • 3.1.4 Uniform - or - Non-uniform Flows.
  • 3.1.5 One, Two - or - Three Dimensional Flows.
  • 3.1.6 Rational - or - Irrational Flows.
  • 3.2 Circulation - or - Vorticity.
  • 3.3 Stream Lines, Flow Field and Stream Tube.
  • 3.4 Velocity and Acceleration in Flow Field.
  • 3.5 Continuity Equation for One Dimensional
    Steady Flow.

2
Fluid Flow Kinematics
3
  • Fluid Kinematics deals with the motion of fluids
    without considering the forces and moments which
    create the motion.

We define field variables which are functions of
space and time Pressure field, Velocity field

Acceleration field,
4
Types of fluid Flow 1. Real and Ideal Flow
If the fluid is considered frictionless with zero
viscosity it is called ideal. In real fluids the
viscosity is considered and shear stresses occur
causing conversion of mechanical energy into
thermal energy
Ideal
Real
Friction 0 Ideal Flow ( µ 0) Energy loss 0
Friction o Real Flow ( µ ?0) Energy loss 0
5
2. Steady and Unsteady Flow
Steady flow occurs when conditions of a point in
a flow field dont change with respect to time (
v, p, H..changes w.r.t. time
steady
unsteady
  • Steady Flow with respect to time
  • Velocity is constant at certain position w.r.t.
    time
  • Unsteady Flow with respect to time
  • Velocity changes at certain position
  • w.r.t. time

6
3. Uniform and Non uniform Flow
Y
Y
x
x
Non- uniform Flow means velocity changes at
certain time in different positions ( depends on
dimension x or y or z(
Uniform Flow means that the velocity is
constant at certain time in different positions
(doesnt depend on any dimension x or y or z(

uniform
Non-uniform
7
y
4. One , Two and three Dimensional Flow
x
Two dimensional flow means that the flow
velocity is function of two coordinates V f(
X,Y or X,Z or Y,Z )
One dimensional flow means that the flow
velocity is function of one coordinate V f( X
or Y or Z )

Three dimensional flow means that the flow
velocity is function of there coordinates V
f( X,Y,Z)
8
4. One , Two and three Dimensional Flow (cont.)
  • A flow field is best characterized by its
    velocity distribution.
  • A flow is said to be one-, two-, or
    three-dimensional if the flow velocity varies in
    one, two, or three dimensions, respectively.
  • However, the variation of velocity in certain
    directions can be small relative to the variation
    in other directions and can be ignored.

The development of the velocity profile in a
circular pipe. V V(r, z) and thus the flow is
two-dimensional in the entrance region, and
becomes one-dimensional downstream when the
velocity profile fully develops and remains
unchanged in the flow direction, V V(r).
9
5. Laminar and Turbulent Flow
  • In Laminar Flow
  • Fluid flows in separate layers
  • No mass mixing between fluid layers
  • Friction mainly between fluid layers
  • Reynolds Number (RN ) lt 2000
  • Vmax. 2Vmean
  • In Turbulent Flow
  • No separate layers
  • Continuous mass mixing
  • Friction mainly between fluid and pipe walls
  • Reynolds Number (RN ) gt 4000
  • Vmax. 1.2 Vmean

Vmean
Vmean
Vmax
Vmax
10
5. Laminar and Turbulent Flow (cont.)
11
Rotational and irrotational flows
The rotation is the average value of rotation of
two lines in the flow. (i) If this
average 0 then there is no rotation and the
flow is called irrotational flow
12
6. Streamline
A Streamline is a curve that is everywhere
tangent to it at any instant represents the
instantaneous local velocity vector.
Stream line equation
Where u velocity component in -X- direction v
velocity component in-Y- direction w velocity
component in -Z- direction
z
w
V
x
u
v
y
13
velocity vector can written as
Where i, j, k are the unit vectors in ve x,
y, z directions
Acceleration Field
  • From Newton's second law,
  • The acceleration of the particle is the time
    derivative of the particle's velocity.
  • However, particle velocity at a point is the same
    as the fluid velocity,

14
Mathematically the total derivative equals the
sum of the partial derivatives
Convective component
Local component
15
Similarly
16
Airplane surface pressure contours, volume
streamlines, and surface streamlines
NASCAR surface pressure contours and streamlines
17
7. Streamtube
  • Is a bundle of streamlines
  • fluid within a streamtube remain constant
  • and cannot cross the boundary of the
    streamtube.
  • (mass in mass out)

18
Types of motion or deformation of fluid element
Linear translation
Rotational translation
Linear deformation
angular deformation
19
8- Rotational Flow Irrotational Flow The rate
of rotation can be expressed or equal to the
angular velocity vector( )
Note
20
The flow is side to be rotational if
The fluid elements are rotating in space (see
Fig. 4-44 )
The flow is side to be irrotational if
The fluid elements dont rotating in space (see
Fig. 4-44 )
21
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22
rotational flow
Irrotational flow
23
9- Vorticity ( ? )
Vorticity is a measure of rotation of a fluid
particale Vorticity is twice the angular velocity
of a fluid particle
24
10- Circulation ( ? )
The circulation ( ? ) is a measure of rotaion
and is defined as the line integral of the
tangential component of the velocity taken around
a closed curve in the flow field.

?
. cos ?
NOTE The flow is irrotational if ?0,
?0, ?0
25
For 2-D Cartesian Coordinates
Y
dy

dx
x
? ? . area
26
Conservation of Mass ( Continuity Equation )
( Mass can neither be created nor destroyed ) The
general equation of continuity for three
dimensional steady flow
z
dz
dx
x
dy
y
27
Net mass in x-direction -

Net mass in y-direction -

Net mass in z-direction -

S net mass mass storage rate



0
28
General equation fof 3-D , unsteady and
compressible fluid Special cases 1- For steady
compressible fluid 2- For incompressible fluid
( ? constant )
Note The above eqn. can be used for steady
unsteady for incompressible fluid
29
3- For 2-D
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